The extragalactic background light (EBL) in the ultraviolet to far-infrared wavelength range is dominated by the emissions from stars in galaxies and reflects the time-integrated history of the light production and reprocessing in the Universe. Direct measurements of the EBL are affected by the interplanetary dust and galactic emission. Hence, the absolute level of EBL is subject to considerable uncertainties. Observations of very high energy (VHE) blazars located at cosmological distances by the Fermi-Large Area Telescope (LAT) and ground-based gamma-ray telescopes (e.g. H.E.S.S., MAGIC, VERITAS, TACTIC) provide a measurement of the EBL that is independent of the direct observations. The interaction of VHE or TeV photons originated from the distant blazars with the low energy EBL photons via e − e + pair-production can be used as a powerful tool to probe the different EBL models in the wavelength range 0.1-1000µm. In this paper, we use two different methods to determine the opacity of the VHE γ-ray photons caused by the low energy EBL photons and study the consequences of six different EBL models. The first method-Model-Dependent Approach, uses various EBL models for estimating the opacity as a function of the source redshift and energy. The second method-Model-Independent Approach, relies on using the simultaneous observations of blazars in the MeV-GeV energy range from the Fermi-LAT and in TeV band from the ground-based Cherenkov telescopes. We make underline assumption that the extrapolation of the LAT spectrum of blazars to TeV energies is either a good estimate or an upper limit for the intrinsic VHE spectrum of the source. We apply this method on the simultaneous observations of a few blazars PKS 2155-304, RGB J0710+591, 1ES 1218+304 and RBS 0413 at different redshifts to demonstrate a comparative study of six prominent EBL models. Opacities of the VHE γ-ray photons predicted by the Model-Independent Approach are systematically larger than the ones estimated from the Model-Dependent Approach using the six EBL models. Therefore, the γ-ray observations of blazars can be used to set a strict upper limit on the opacity of the Universe to the VHE γ-rays at a given redshift.